I have the next differential equation
\begin{eqnarray} A\frac{dh}{dt}=-\sqrt{2gh}; \hspace{2cm} h(0)=h_{0} \end{eqnarray} Where $A,h_{0},g$ are positive constants,so I need to pass this differential equation to a linear and solve by Laplace transform but I can't see some apropiate variable change for this. I was trying to resolve the original differential equation, this solution is
\begin{eqnarray} h(t)=h_{0}-\frac{\sqrt{2gh_{0}}}{A}t+\frac{g}{2A}t^{2} \end{eqnarray} Do you know some variable change, to convert this non-linear differential equation to a linear? Thank you for your comments or hint.